GPU Acceleration of Melody Accurate Matching in Query-by-Humming

Algorithm 2

Parallel implementation for calculating the matrix 𝐷 PDTW (𝑄,𝑃).

Input:  Humming pitch sequence 𝑄=(𝑞₁,𝑞₂,…,𝑞_𝑚)

     Frame-based candidate pitch sequence 𝑃^′=(𝑝^′₁,𝑝^′₂,…,𝑝^′_𝑡)

Output: Cost matrix D

(1) Initialize the first two rows and columns of the matrix D

(2) for  𝑗=2  to  𝑡  do

(3)  for  𝑖=2  to  𝑚  parallel do

(4)   calculate 𝐷(𝑖,𝑗)

(5)  end for

(6)  synchronize( )

(7) end for

(8) return  D